Locals are suspicious about the cause of death
Mr Eluay was on bail while being tried for treason.
The funeral took place on Saturday in Mr Eluay's home town of Sentani, 50 kilometres west of the provincial capital Jayapura.
He was buried at a football field redesignated as a Papuan Heroes cemetery.
The funeral was originally planned for 1 December - the 40th anniversary of the declaration of independence by separatists.
Last respects
Tribal leaders wearing feather costumes performed traditional dances and paid their last respects to Mr Eluay.
His coffin, draped in the pro-independence Morning Star flag, was held up by members of the Papua Task Force militia.
Weeping mourners showered the coffin with flowers, shouting: "Father, don't leave us behind!"
"I feel a great loss because the land of Papua has lost its leader. Who else will lead Papua?" said kindergarten teacher Thinea Okowally.
'Unnatural' death
Mr Eluay's body was found on Sunday inside his crushed car at the bottom of a ravine, hours after he was abducted.
An autopsy revealed he had been asphyxiated, and police investigating the incident have described the death as "unnatural". Mr Eluay's driver is still missing.
The Indonesian military has denied accusations by Mr Eluay's family that they carried out the killing.
Mr Eluay's sister Hindom said local people believed the military had been involved.
Mr Eluay, 64, had recently rejected moves by the Indonesian Government to grant the province a degree of autonomy.
The new laws, which come into effect next month, will give Irian Jaya a greater share of its rich mineral resource revenues.
The government has ruled out full independence for the province, which lies on the western half of New Guinea island, but it hopes more autonomy will end nearly 40 years of separatist fighting there.
The province will change its name to Papua, and it will be able to fly its own independence flag and use its own anthem.
Mr Eluay and four members of the Papua Presidium, the pro-independence umbrella group which he headed, had been on trial, charged with treason for trying to set up an independent state of West Papua.